To me, Bart seemed clear-headed, not whacked out on medication for his wound. So he was apparently in his right mind when he inferred that he had no other brothers except for Bret.
And yet Brent Maverick, as played by Robert Colbert in two 'Maverick' episodes, was presented as one of the Maverick brothers on the show. In one of those episodes, "The Forbidden City", Jack Kelly also appeared. And he probably introduced Brent as his brother. There's also the publicity picture still floating around of Kelly and Roger Moore in costume as Bart and Beau with Colbert as Brent (looking like a poor man's Bret... a wooden, robotic Bret.) Had Brent tried to pass himself off as a Maverick without official support, Toobworld Central was ready to play it out four different ways. One, that if he was a Maverick brother, he was Beau's brother. He wouldn't need a British accent - Beau picked that up as an affectation after spending a decade in England, banished for an indiscretion during the Civil War. (He became a war hero.)
The second splainin was that he was passing himself off as a Maverick, but was in fact Cherokee Dan Evans, the character he played in the episode "Hadley's Hunters" (one of the greatest contributions to TV crossovers ever.)
The third option would be to claim that he was an android similar to Hymie the Robot from 'Get Smart'. (Dick Gautier - now there's an actor who could have pulled off that 'Maverick' mojo!) But O'Bviously we'd never fight for that pozz'bility. Otherwise we're wandering into the territory of "The Wild Wild West Revisited". Blerg. Finally, and the most enticing to a fan of the TV Universe mosaic, he was actually Dr. Doug Phillips, a time-traveling researcher at the top-secret Project Tick-Tock underneath the Arizona desert, as seen in 'The Time Tunnel'. For just those two episodes he had been separated from his associate Dr. Tony Newman and so was hiding in plain sight until they could be reunited. To get Bart to go along with the idea must have cost Dr. Phillips something in return....
But sadly, Brent was presented as a son of Beauregard "Pappy" Maverick and that puts the kibosh on all those theories, while at the same time it presents a Zonk with Bart's statement that he and Bret were the only brothers.
But it's easily splained away: Brent is a half-brother to Bret and Bart, the product of one of Pappy's indiscretions. Talk about a "Seed Of Deception"! And so, at the time of the episode, the Maverick boys didn't know they had a brother.